Technical Field
The present invention relates to a device, method and non-transitory computer readable media to guide a drill during well drilling, and to guide a drill during well drilling for water injection well used to improve the production of hydrocarbons from an oil reservoir.
Description of the Related Art
The “background” description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly or impliedly admitted as prior art against the present invention.
The inflow performance relationship (IPR) represents a crucial factor in estimating and evaluating the reservoir behavior. It is of importance to production and reservoir engineers. The IPR is synonymous with a quantity called the productivity index (PI), or the injectivity index (II) for injection wells. It is a relationship between the reservoir flow/injection rate and the flowing/injection bottom-hole pressure (PWF/PWJ). For water supply and water injection wells, it is a function of many reservoir parameters like reservoir thickness, permeability, drainage radius, and skin as well as well geometry. For every reservoir with different rock and fluid properties and different types of wells, the PI is calculated according to distinct process using a particular equation. Most of the published work and methods were developed for vertical, single horizontal and multilateral wells. Slanted models are uncommon for hydrocarbon wells. The most widely used models for calculating PI for slanted wells express the well deviation effect into a pseudo-skin of a vertical well's IPR.
Reservoirs put on production will experience a decline in its pressure with time unless there is a strong pressure support from an aquifer or a gas cap. In absence of this natural support, artificial pressure maintenance is needed to boost and preserve the reservoir energy and to keep the pressure above the bubble point to prolong profitability of the reservoir. Water flooding is the most common and successful operation to achieve this goal. Generally, water flooding operations involve injecting huge amounts of water into the reservoir. This amount of water can be supplied form a nearby water formation or be treated sea water; so some wells are drilled into water-producing formation and are used as water supply for hydrocarbon production.
In oil fields, oil and water wells are drilled in many ways in order to reach a pay zone. These wells can be vertical, directional, horizontal or a combination of any of these geometries. Some conditions may dictate the path of the well like lithology, engineering aspects, economics, location etc. For example, in offshore rigs it is favorable to drill wells with an angle (slanted), highly deviated or horizontally to drain the reservoir. Near populated areas, wells are sidetracked from a distance to reach the reservoir. In some cases drilling a well may not go as planned and the well penetrates the reservoir with an angle from one or more bedding planes. Generally, slanted wells are those wells with an angle between 15° to 60°, whereas wells with an angle greater than 60° are considered highly-deviated. Slanted wells' most important advantage is to increase the contact area with the reservoir in order to achieve higher productivity/injectivity. Though, the cost of drilling slanted or horizontal well is much higher than drilling a well vertically.
For a vertical well producing from a single-oil reservoir, the productivity index (PI) can be given from Darcy's law as:
                    PI        =                                            q              o                                                      P                e                            -                              P                wf                                              =                      kh                          141.2              ⁢                                                          ⁢                              B                o                            ⁢                                                μ                  o                                ⁡                                  [                                                            ln                      ⁡                                              (                                                                              r                            e                                                                                r                            w                                                                          )                                                              +                    s                                    ]                                                                                        (        1        )            
Where PI is Productivity Index (STB/Day/PSI), qo is Oil Production (STB/D), Pe is Reservoir Pressure (PSI), Pwf is Flowing Bottom Hole Pressure (PSI), k is permeability (MD), h is Reservoir Thickness (FT), Bo is Oil formation Volume Factor (RB/STB), μo is Oil Viscosity (CP), re is Drainage Radius (FT), rw is Wellbore Radius (FT), s is Skin Factor (Dimensionless).
                    II        =                                            q              w                                                      P                wfi                            -                              P                e                                              =                      kh                          141.2              ⁢                                                          ⁢                              B                w                            ⁢                                                μ                  w                                ⁡                                  [                                                            ln                      ⁡                                              (                                                                              r                            e                                                                                r                            w                                                                          )                                                              +                    s                                    ]                                                                                        (        2        )            
For Water Injection, the injectivity index (II) can be determined as: Where II is Injectivity Index (STB/Day/PSI), qw is Water Injection (STB/D), Pe is Reservoir Pressure (PSI), Pwfi is Bottom Hole Injection Pressure (PSI), Bw is Water formation Volume Factor (RB/STB), and μw is Water Viscosity (CP).
The right-hand side of equations (1) and (2) is identical for a water supplier and a water injector, because in both cases the fluid is water. As for slanted and highly-deviated wells, Choi et al. (2008) disclosed that “no analytical correlations identified for slanted well geometry; instead, three correlations for deviation skin were applied to combine with any correlation made for the vertical well to calculate PI for slanted wells”. See Choi, S. K., Ouyang, L. B. and Huang, W. S., “A Comprehensive Comparative Study on Analytical PI/IPR Correlations”, SPE 116580 presented at the 2008 SPE Annual Technical Conference and Exhibition of the Society of Petroleum Engineering held in Denver, Colo., USA, 21-24 Sep. 2008, incorporated herein by reference in its entirety. Cinco et al. (1975) proposed a simple correlation for slanted skin based on the study of unsteady state flow of a slightly compressible fluid. See Cinco, H., Miller, F. G., and Ramey, H. J., “Unsteady-State Pressure Distribution Created By a Directionally Drilled Well”, JPT, p 1392-1400, November, 1975, incorporated herein by reference in its entirety. This correlation is valid for well deviation angles between 0 to 75°:
                                          s            θ                    =                                    -                                                (                                                            θ                      w                      ′                                        41                                    )                                2.06                                      -                                                            (                                                            θ                      w                      ′                                        56                                    )                                1.865                            ⁢                                                log                  10                                ⁡                                  (                                                            h                      D                                        100                                    )                                                                    ⁢                                  ⁢        Where        ⁢                                  ⁢                                            θ              w              ′                        =                                          tan                                  -                  1                                            (                                                                                          k                      v                                                              k                      h                                                                      ⁢                                  tan                  ⁡                                      (                    θ                    )                                                              )                                ,                                    h              D                        =                                          h                                  r                  w                                            ⁢                                                                    k                    h                                                        k                    v                                                                                                          (        3        )            kv is the Vertical Permeability (MD), kh is Horizontal Permeability (MD), θ is the Deviation Angle (Degree), h is the Reservoir Thickness (FT).
Besson (1986) proposed another slanted well skin correlation from the results of a semi-analytical simulator. See Besson, J., “Performance of Slanted and Horizontal Wells on an Anisotropic Medium”, SPE 20965, October 1986, incorporated herein by reference in its entirety. For isotropic reservoir and slant angles between 0° to 90°:
                              s          θ                =                              ln            ⁡                          (                                                4                  ⁢                                      r                    w                                                  L                            )                                +                                    h              L                        ⁢                          ln              (                                                Lh                                                  4                  ⁢                                      r                                          w                      ⁢                                                                                                                                                      )                                                          (        4        )            and for anisotropic reservoir:
                                          s            θ                    =                                    ln              ⁡                              (                                                                            4                      ⁢                                              r                        w                                                              L                                    ⁢                                      1                                          ∝                      γ                                                                      )                                      +                                          h                                  γ                  ⁢                                                                          ⁢                  L                                            ⁢                              ln                (                                                                            Lh                                                              4                      ⁢                                              r                        w                                                                              ⁢                                                            2                      ⁢                      α                      ⁢                                              γ                                                                                    1                      +                                              1                        /                        γ                                                                                            )                                                    ⁢                                  ⁢        where        ⁢                                  ⁢                              α            =                                                            k                  h                                /                                  k                  v                                                              ,                      γ            =                                                            1                                      α                    2                                                  +                                                                            h                      2                                                              L                      2                                                        ⁢                                      (                                          1                      -                                              1                                                  α                          2                                                                                      )                                                                                                          (        5        )            and L is the well length.Rogers and Economides (1996) presented an expression for the pseudo-skin as:
                              s          θ                =                                            -              1.64                        ⁢                                                  ⁢                                          sin                ⁢                                                                  ⁢                                  θ                  1.77                                ⁢                                  h                  D                  0.184                                                            I                ani                0.821                                      ⁢                                                  ⁢            for            ⁢                                                  ⁢                          I              ani                                <          1                                    (        6        )                                                      s            θ                    =                                                    -                2.48                            ⁢                                                          ⁢                                                sin                  ⁢                                                                          ⁢                                      θ                    5.87                                    ⁢                                      h                    D                    0.152                                                                    I                  ani                  0.964                                            ⁢                                                          ⁢              for              ⁢                                                          ⁢                              I                ani                                      >            1                          ⁢                                  ⁢        Where        ⁢                                  ⁢                                            I              ani                        =                                                            k                  h                                                  k                  v                                                              ,                                    k              h                        =                                                            k                  x                                ⁢                                  k                  y                                                              ,                                    h              D                        =                          h                              r                                  w                  ⁢                                                                                                                                                (        7        )            See Roger, E., and Economides, M., “The Skin due to Slant of deviated Wells in Permeability-Anisotropic Reservoirs”, SPE 37068, November 1996, incorporated herein by reference in its entirety. Slanted wells produce more fluid from the reservoir than vertical wells do because of the increased area open to flow. Similarly for the injection wells, they achieve higher injectivity and perform better in compared to vertical wells. Cinco, Besson and Economides expressed the effect of well slant into the form of pseudo-skin.
The present disclosure is concerned with the performance of wells that operate as slanted and highly-deviated water supply and water injection wells.